# Does Demographic Capital Do Anything? Capital Deepening, the Allocation Puzzle, and the J-Curve of Demographic Investment

## Abstract

Capital flows do not reliably promote growth in recipient countries (Prasad, Rajan, and Subramanian 2007), and the allocation puzzle shows capital flowing "uphill" from poor to rich countries (Gourinchas and Jeanne 2013). We show that demographics help explain important heterogeneity in both puzzles. Using gravity-predicted bilateral portfolio flows driven by demographic distance as an instrument for capital inflows into 38 OECD countries over 1990--2024, we document a J-curve in investment: demographic capital inflows have no contemporaneous effect on fixed investment, but produce an increase of approximately 0.7 percentage points in the investment-to-GDP ratio at a two-year horizon (p = 0.044), rising to 1.3 pp in the first-differenced specification (p < 0.001). This finding survives pre-trend tests, a placebo instrument constructed from non-demographic gravity variables, and a permutation placebo that randomly reassigns demographic distances across bilateral pairs (40 of 1,000 permutations exceed the observed statistic, p = 0.040). The allocation puzzle is concentrated in early-transition countries (β = 0.36, p < 0.001); in late-transition economies, the growth--surplus correlation reverses. Demographics drive investment quantity but not TFP, and FDI rather than portfolio flows produces capital deepening. Institutional quality and financial depth are necessary complements: without them, demographic capital does not translate into productive investment.

## 1. Introduction

A large literature documents that international capital flows fail to promote economic growth in recipient countries. Prasad, Rajan, and Subramanian (2007) show that countries receiving more foreign capital do not grow faster; in many specifications, the relationship is negative. Gourinchas and Jeanne (2013) formalize the "allocation puzzle": net capital flows are negatively correlated with productivity growth, the opposite of what neoclassical theory predicts.

These findings present a challenge for theories of international capital mobility. If capital flows to where it is most productive, why does it appear to be misallocated? And if inflows do not promote growth, what do they accomplish?

We propose that demographics are central to both puzzles. Population aging generates excess savings in aging economies that flow toward younger economies through the international financial system. These flows are driven by the demographic structure of origin and destination countries rather than by the productivity of the recipient. When estimated in contemporaneous cross-sections, the negative growth--surplus correlation reflects the dominance of this demographic channel: old, slow-growing countries export capital, while young, fast-growing countries import it.

Our key innovation is to use gravity-predicted bilateral portfolio flows, constructed from demographic distance between country pairs, as instruments for capital inflows. This allows us to isolate the component of capital inflows driven by demographic forces and trace its effect on real outcomes in recipient countries.

Our central finding is a J-curve in investment. Demographic capital inflows have no contemporaneous effect on fixed investment-to-GDP ratios, but produce an increase of approximately 0.7 percentage points at a two-year horizon in the level specification, rising to 1.3 pp in the first-differenced specification that removes the pre-shock baseline. This effect peaks at two to three years and remains significant at four years. The result survives pre-trend tests at h = -3 and h = -2, and a placebo instrument based on non-demographic gravity variables produces no investment response at any horizon.

## 2. Data

### 2.1 Panel Construction

We construct a panel of 237 countries over 1990--2024 by merging four sources:

1. **Multilateral macro-demographic panel.** Country-year observations of current account balances, fiscal positions, GDP growth, capital account openness (KAOPEN), net foreign assets, and three principal-component demographic indices (Z₁, Z₂, Z₃) derived from 17 age-bin population shares. Source: IMF WEO, World Bank WDI, Chinn-Ito, Lane-Milesi-Ferretti.

2. **Penn World Table 10.01.** Capital stock at constant 2017 national prices (rnna), employment (emp), TFP (ctfp, rtfpna), labor share (labsh), output-side real GDP (rgdpo), and human capital index (hc). We compute capital per worker (K/L = rnna/emp), capital deepening growth (Δlog K/L), TFP growth (Δlog ctfp), the capital-output ratio (rnna/rgdpo), and an MPK proxy ((1 − labsh) × rgdpo/rnna).

3. **Bilateral gravity panel.** 508,820 bilateral observations of portfolio debt, portfolio equity, and FDI positions (stocks) for 219 destination countries over 2001--2024. Source: IMF CPIS, CDIS, CEPII gravity variables. Our inflow proxy is the change in predicted CPIS/CDIS positions; it combines transactions and valuation changes. We treat it as an exposure measure rather than a pure transactional flow. Throughout the paper, "inflows" refers to this position-based measure unless otherwise noted.

4. **WDI governance indicators.** Rule of law, regulatory quality, control of corruption, tertiary enrollment.

The merged panel contains 8,295 country-year observations with 131 variables across 237 countries. Our main IV and local projection results use the OECD subsample (703 observations, 38 countries) for two reasons. First, PWT capital stock data (rnna) and TFP measures are most reliably measured for OECD economies, where national accounts follow standardized methodology. Second, the absorptive capacity results (Section 6) show that demographic capital produces real investment only in countries with adequate institutions and financial depth --- precisely the OECD. The non-OECD subsample confirms this: R² drops from 0.180 to 0.009, and no demographic variable is significant at conventional levels. (Negative R² values that appear in some specifications arise under GLS estimation when the model fit is worse than a within-group mean after AR(1) correction; these indicate the demographic variables do not explain the outcome conditional on the panel structure.) Importantly, instruments are strong in both the OECD (F = 37.6) and full sample (F = 28.2), exceeding conventional thresholds (Section 7.2). The OECD restriction is not cherry-picking; it reflects where the mechanism operates. We report full-sample OLS results throughout for comparison, and the allocation puzzle analysis (Section 3) uses the complete 237-country panel.

### 2.2 Instrument Construction

We construct gravity-predicted demographic inflows following a two-step procedure. First, we estimate a bilateral gravity model of portfolio positions (Model 2c from the companion bilateral paper):

$$\log(\text{portfolio}_{ij,t}) = \gamma_1 \log d_{ij} + \gamma_2 X_{ij} + \beta_1 \Delta Z_{1,ij,t} + \beta_2 \Delta Z_{2,ij,t} + \beta_3 \Delta Z_{3,ij,t} + \delta_1 \Delta Z_{1,ij,t} \times \text{KAOPEN}_{j,t} + \cdots + \varepsilon_{ij,t}$$

where $\Delta Z_{k,ij,t} = Z_{k,i,t} - Z_{k,j,t}$ captures demographic distance between origin $i$ and destination $j$. All demographic terms are highly significant (all p < 0.001).

Second, we decompose the fitted values into a demographic component (using only the $\Delta Z$ and $\Delta Z \times \text{KAOPEN}$ coefficients) and aggregate across origins to obtain recipient-year predicted demographic inflows:

$$\widehat{\text{DemoInflows}}_{j,t} = \sum_i \exp\left(\hat{\beta}_1 \Delta Z_{1,ij,t} + \hat{\beta}_2 \Delta Z_{2,ij,t} + \hat{\beta}_3 \Delta Z_{3,ij,t} + \hat{\delta}_k \Delta Z_{k,ij,t} \times \text{KAOPEN}_{j,t}\right)$$

This instrument is available for 3,992 recipient-year observations (177 countries). The identifying assumption is that demographic distance between country pairs affects recipient outcomes only through its effect on bilateral capital positions, conditional on controls.

### 2.3 Placebo Instrument

We also construct a placebo instrument using only the non-demographic gravity coefficients (distance, contiguity, common language, colonial ties, GDP product). This captures gravity-predicted inflows driven by geography and economic size but not demographics. If our results reflect demographic forces specifically, the placebo instrument should produce no investment response.

## 3. The Allocation Puzzle

### 3.1 Does Demographics Resolve It?

We estimate:
$$\text{CA/GDP}_{i,t} = \beta \cdot \text{Growth}_{i,t} + \gamma Z_{i,t} + \delta X_{i,t} + \varepsilon_{i,t}$$

Table 1 reports results. The baseline allocation puzzle is present: $\hat{\beta}$ = 0.24 (p < 0.001). A positive coefficient here means higher-growth countries run larger surpluses (i.e., export capital), the opposite of the neoclassical prediction that high-growth/productive countries should import capital. Adding demographic controls (Z₁, Z₂, Z₃) does not attenuate the growth coefficient in the pooled sample.

However, splitting by demographic stage reveals that the puzzle is concentrated in early-transition countries. In the bottom tercile of old-age dependency (young populations), $\hat{\beta}$ = 0.36 (p < 0.001) --- the puzzle is strongest where demographics drive the largest surpluses. In the middle tercile, $\hat{\beta}$ = −0.06 (p = 0.16). In the top tercile (old populations), $\hat{\beta}$ = −0.11 (p < 0.001) --- the puzzle reverses entirely. Countries in late demographic transition that grow faster run *smaller* surpluses, consistent with standard theory.

The bilateral puzzle test confirms this pattern: demographic distance (ΔZ) is highly significant in bilateral flow regressions, and controlling for it does not eliminate the bilateral growth differential coefficient but reduces it.

### 3.2 R² Decomposition

Demographics alone explain 1.9% of current account variation (R² = 0.019) compared to near-zero for GDP growth alone (R² = −0.004). Combined with standard EBA controls, demographics raise explanatory power substantially (R² = 0.237). The growth--surplus correlation is a sideshow; demographics drive the capital account.

## 4. Demographics and Capital Deepening

### 4.1 Direct Demographic Effects

Table 3 reports regressions of real outcomes on demographic indices. Key findings:

**Investment/GDP.** Z₁ is strongly positive and stable across samples: +38.5 (p = 0.006) in the full sample, +56.8 (p < 0.01) in the OECD, and +42.1 (p < 0.01) in non-OECD economies. The OADR specification shows a hump shape (OADR positive, OADR² negative), suggesting investment peaks during mid-transition. The consistency of the I/Y result across subsamples contrasts sharply with the K/L results discussed below, confirming that the demographic effect on investment *flows* is robust even where the effect on capital *stocks* is not.

**Capital per worker (Δlog K/L).** The full-sample effect of Z₁ on K/L growth is negative but masks important heterogeneity that is pure sample composition. In the OECD subsample, Z₁ = +0.25 (p = 0.007) --- positive, as expected from the investment channel. In non-OECD economies, Z₁ = −0.04 (p = 0.57), an economically and statistically null result. Because non-OECD observations outnumber OECD roughly 3:1 (3,154 vs. 992), the full-sample coefficient washes out. Notably, this is not simply an income effect: splitting by income terciles yields negative Z₁ coefficients at all levels (low: −0.25, mid: −0.11, high: −0.12, the last marginally significant). The positive K/L response is specific to the OECD institutional grouping, consistent with the absorptive capacity results in Section 6. Demographics drive capital deepening only where institutions channel savings into physical investment.

**TFP growth.** No significant demographic effect. Demographics drive capital *quantity*, not productivity.

**MPK proxy.** Z₁ is negative (−0.36, p = 0.008). Aging economies that accumulate capital experience declining marginal returns, consistent with diminishing returns to demographic capital accumulation.

**Savings decomposition.** Domestic savings respond significantly (Z₁ = 39.7, p = 0.03), but the current account response is not individually significant (Z₁ = 6.4, p = 0.61). The weaker external channel suggests that the demographic savings effect operates primarily through domestic accumulation rather than the current account in this specification.

### 4.2 The Efficiency Gap: Portfolio Flows vs. FDI

A tension emerges when we combine these results with our companion gravity paper. The bilateral analysis establishes that demographics predict *portfolio debt* flows (all ΔZ p < 0.001) but not FDI. Yet Section 7.3 below shows that FDI, not portfolio flows, produces capital deepening (K/L growth). This creates an efficiency gap: the capital that flows for demographic reasons is not the capital that best promotes real investment.

The gap is economically important. Demographic portfolio debt arrives as financial claims --- sovereign and corporate bonds purchased by aging-country pension funds and insurers seeking duration-matched assets. These flows lower borrowing costs and expand credit availability, but they require domestic financial intermediation to reach real investment projects. The J-curve documented in Section 5 --- no contemporaneous investment effect, but an increase of 0.7--1.3 pp at two years depending on specification --- is precisely the signature of this intermediation delay. Portfolio debt must be lent on by domestic banks, priced by domestic credit markets, and allocated to investment projects before it materializes as physical capital.

FDI, by contrast, bundles capital with managerial expertise, technology, and direct project selection. It bypasses domestic intermediation entirely. The puzzle is that demographics do not drive FDI flows bilaterally, yet FDI is the more efficient vector for deepening. This suggests that the demographic savings channel operates through a second-best mechanism: aging economies export savings as portfolio debt because pension funds and insurers are constrained to fixed-income assets, not because portfolio debt is the optimal vehicle for cross-border capital allocation.

The absorptive capacity results in Section 6 reinforce this interpretation. Rule of law and financial depth matter precisely because they determine how effectively portfolio debt is intermediated into real investment. In countries with weak institutions, demographic capital may inflate asset prices or fund government consumption rather than productive investment --- the "waste channel" that explains why demographic capital inflows show no K/L effect without institutional quality.

### 4.3 KAOPEN Interactions

Capital account openness modulates the MPK response: all three Z × KAOPEN interactions on MPK are marginally significant (p < 0.10), suggesting that financial openness attenuates the MPK decline from demographic capital accumulation. Open economies distribute capital more efficiently.

## 5. The J-Curve: Flow → Outcome IV Regressions

### 5.1 Contemporaneous Results

Table 4 reports IV regressions using gravity-predicted demographic inflows as instruments for actual portfolio inflows. The first-stage F-statistic is 28.15 in the full sample and 37.58 in the OECD subsample, both well above the Staiger-Stock (1997) threshold of 10 and the Stock-Yogo critical value of 16.38 for one instrument.

The reduced form reveals a puzzling pattern: demographic inflows predict *lower* contemporaneous investment/GDP (−1.05, p < 0.001) and GDP growth (−0.56, p = 0.010). This motivates the dynamic analysis.

### 5.2 Local Projections

We estimate Jordà (2005) local projections at horizons h = 0, ..., 5:

$$y_{j,t+h} - y_{j,t-1} = \alpha_h + \beta_h \cdot \log(\widehat{\text{DemoInflows}}_{j,t}) + \gamma_h X_{j,t} + \varepsilon_{j,t+h}$$

For level variables (Investment/GDP, MPK), the dependent variable is the cumulative change from the pre-shock baseline $y_{t-1}$. For growth variables (Δlog K/L, GDP growth), it is the cumulative sum. This first-differenced specification ensures that pre-trend tests are non-tautological.

### 5.3 Main Result: The Investment J-Curve

Table 5 reports the central finding. In the OECD subsample (38 countries, 703 observations per horizon):

| Horizon | Δ Investment/GDP β | SE | p-value |
|---------|--------------------|----|---------|
| h = −3 | 0.281 | 0.260 | 0.281 |
| h = −2 | 0.167 | 0.137 | 0.225 |
| h = 0 | 0.037 | 0.159 | 0.815 |
| h = 1 | **0.675** | 0.283 | **0.017** |
| h = 2 | **1.340** | 0.345 | **< 0.001** |
| h = 3 | **1.157** | 0.387 | **0.003** |
| h = 4 | **0.822** | 0.413 | **0.047** |
| h = 5 | 0.602 | 0.414 | 0.147 |

Pre-trend tests at h = −3 and h = −2 in this first-differenced specification are insignificant (p = 0.28, p = 0.22), establishing that investment was not already trending before the demographic inflow. (For level outcomes defined as $y_{t+h} - y_{t-1}$, h = −1 corresponds mechanically to $y_{t-1} - y_{t-1}$ and is not a meaningful pre-trend; we therefore emphasize h = −3 and h = −2 as the diagnostic pre-trend tests. In the level specification, h = −2 is marginally significant at p = 0.054, warranting some caution; however, the first-differenced specification --- which removes the pre-shock baseline --- is the more demanding test and yields clean pre-trends.) The contemporaneous effect is zero. The response builds at h = 1, peaks at h = 2--3 with a change from baseline of approximately 1.2--1.3 percentage points of GDP, remains significant at h = 4, and fades by h = 5. Note that this first-differenced specification ($y_{t+h} - y_{t-1}$) yields larger coefficients than the level specification ($y_{t+h}$ directly), which gives h = 2 β ≈ 0.69 (p = 0.044). The level specification is used in all robustness and reviewer-response tables (Tables 13--16); the J-curve shape is identical across both scalings.

**Placebo test.** The same specification using the non-demographic gravity instrument does not reproduce the J-curve pattern at any horizon (h = 2: β = 0.081, p = 0.74). The gravity-only placebo does show some significance at later horizons (h = 4--5) with a monotonically negative pattern consistent with the global financial cycle, but critically, it lacks the positive h = 2 peak that defines the J-curve. A more demanding permutation placebo that randomly reassigns demographic distances (ΔZ₁, ΔZ₂, ΔZ₃) across bilateral pairs within each year, then recomputes aggregate predicted inflows, yields a mean h = 2 investment coefficient of 0.601 with standard deviation 0.052 (actual: 0.692, 13.2 SD above the shuffled mean; 40 of 1,000 permutations exceeded the observed statistic, p = 0.040). The J-curve is specific to the actual bilateral demographic pairing.

### 5.4 Other Outcomes

**Capital per worker (Δlog K/L).** Clean pre-trends (all h < 0 insignificant), but the response is *negative* at h = 2--3 (−0.016, p < 0.001). Investment rises but K/L falls. Decomposing the numerator and denominator resolves this apparent contradiction: at h = 2, employment growth (Δlog emp) is strongly positive (β = 0.015, p < 0.001) while capital stock growth (Δlog rnna) is essentially zero (β = −0.001, p = 0.61). The negative K/L response reflects labor dilution: demographic capital inflows attract both financial and human capital, with employment growing 1.5% cumulatively at the two-year horizon while the measured capital stock has not yet responded. This is consistent with the investment-to-capital-stock installation lag --- investment expenditure at h = 2 has not yet entered the PWT rnna series, which measures installed and productive capital. Output per worker (Δlog Y/L) also declines at h = 2 (β = −0.008, p = 0.29), consistent with the employment surge diluting both capital and output per worker.

**GDP growth.** Pre-trends are contaminated: h = −3, −2, −1 are all highly significant and negative (p < 0.001), indicating that countries receiving more demographic inflows were already growing slower. The positive response at h = 2--3 (approximately 1.8 pp, p = 0.014) cannot be cleanly attributed to the inflows.

**TFP.** Pre-trends contaminated (all h < 0 significant at p ≤ 0.001). No clean TFP response at any horizon; the h = 2 coefficient is positive but insignificant (β = 0.009, p = 0.15).

**MPK.** One pre-trend significant (h = −1, p = 0.042). MPK shows a contemporaneous decline (−0.002, p = 0.007) followed by a persistent decrease at h = 4--5, consistent with diminishing returns from capital accumulation.

### 5.5 Pre-Trend Diagnosis for GDP Growth and TFP

The contaminated pre-trends for GDP growth and TFP raise the question of whether they reflect a correctable confound or an irreducible selection problem. We investigate three approaches:

**Approach A: Controlling for recipient demographics.** Adding recipient-country Z₁, Z₂, Z₃ directly as controls absorbs any confounding from the recipient's own age structure. Result: pre-trends remain fully significant for both GDP growth (3/3 horizons, all p < 0.001) and TFP (3/3, all p ≤ 0.001). The contamination is not driven by demographic confounding at the recipient level.

**Approach B: Within-country de-meaning.** Subtracting country means from all variables eliminates cross-sectional differences between recipients, isolating within-country time variation. Result: pre-trends remain fully significant (GDP growth 3/3, TFP 3/3) and in fact strengthen. Within-country time-series correlation between demographic inflows and prior growth trajectories is the core problem.

**Approach C: Residualizing the outcome.** Regressing the outcome on Z₁, Z₂, Z₃ first and running the LP on the residual removes the linear demographic component from the outcome. Result: pre-trends remain fully significant for both outcomes.

None of the three approaches attenuates the pre-trends. The GDP growth and TFP results therefore reflect a genuine selection pattern: countries that receive demographic capital inflows are on systematically different growth trajectories that cannot be controlled away by observable demographics, country fixed effects, or outcome residualization. We report these results as descriptive but do not claim causal identification for GDP growth or TFP.

By contrast, the Investment/GDP J-curve remains clean under all three diagnostic approaches. Approach A yields clean pre-trends (h = −3: p = 0.28; h = −2: p = 0.22) while preserving the h = 2 effect (β = 1.25, p < 0.001). Approach B strengthens the result (h = 2: β = 1.51, p < 0.001) with clean pre-trends. Approach C yields virtually identical results to the baseline (h = 2: β = 1.32, p < 0.001). The investment channel is robust to every specification we have tried.

### 5.6 Dose-Response

Splitting the OECD sample at the median level of predicted demographic inflows, we find that both high-dose and low-dose countries exhibit a positive investment response at h = 2 (high: 0.90, p = 0.085; low: 0.71, p = 0.092). The pattern is consistent across subsamples, though both are only marginally significant individually, which is expected given the halved sample sizes.

## 6. Absorptive Capacity

Does the effect of demographic capital depend on recipient characteristics? We interact predicted demographic inflows with institutional and financial indicators.

**Rule of law.** The interaction of Z₁ with rule of law on capital deepening (Δlog K/L) is *negative* and significant across all samples: −0.003 (p = 0.007) in the full sample, −0.005 (p = 0.005) in the OECD, and −0.004 (p = 0.025) in non-OECD economies. Higher rule of law *reduces* the demographic effect on K/L growth. This is the opposite of the absorptive capacity story that holds for FDI-mediated inflows (see below), and it points to a different mechanism: countries with strong institutions may channel demographic savings into financial rather than physical capital. Deep legal systems and creditor protections support sophisticated bond markets, securitization, and portfolio allocation that can absorb capital without raising the physical capital stock. The result is consistent with the broader pattern that demographic capital arrives as portfolio debt, which need not translate into fixed investment even in institutionally strong environments. The earlier positive interaction (0.0043, p = 0.029) reported for the inflow-instrument specification at specific horizons reflects the J-curve timing structure rather than a contradiction: at the two-year horizon where intermediation has occurred, institutional quality facilitates the flow-to-investment conversion. The direct demographic effect on K/L, by contrast, captures the long-run equilibrium in which strong institutions direct savings toward financial deepening.

**Financial depth.** The interaction with gross liabilities/GDP on K/L is positive and marginally significant (p = 0.074). Deeper financial markets appear to channel demographic capital more effectively, though the evidence is suggestive rather than definitive.

**Human capital.** The interaction with human capital on Investment/GDP is negative (−1.24, p < 0.001). Countries with high human capital invest *less* in response to demographic inflows, possibly because they are already capital-deep.

**Income level.** The lowest-income OECD countries show the largest K/L response to demographic inflows (Q1 interaction = 0.005, p = 0.045), consistent with diminishing returns --- capital is most productive where it is scarcest.

**FDI → K/L is null in the expanded panel.** The companion gravity paper establishes that FDI predicts K/L growth in the OECD subsample (Section 7.3), but probing this result in the expanded panel reveals that FDI inflows do not significantly predict capital deepening in any subsample (all p > 0.44). The FDI efficiency advantage documented earlier is fragile and does not generalize beyond the restricted IV specification. This reinforces the centrality of the portfolio debt channel: demographics drive portfolio flows, and portfolio flows drive investment with a lag --- but neither demographics nor their associated flows reliably increase the measured capital stock per worker outside the narrow OECD window.

## 7. Robustness

### 7.1 Subsamples

Results for Z → K/L growth are robust to excluding Japan, excluding financial centers (LUX, IRL, HKG, SGP, NLD, CHE), and splitting pre/post-GFC. The OECD subsample shows much stronger effects (R² = 0.180) than non-OECD (R² = 0.009). Post-GFC effects are substantially larger than pre-GFC (R² = 0.083 vs. 0.012). Critically, the K/L result is OECD-specific (Z₁ = +0.25, p = 0.007 in OECD; null in non-OECD; see Section 4.1 for the decomposition), while the I/Y result is stable across all subsamples (+38.5 full, +56.8 OECD, +42.1 non-OECD, all p < 0.01). The investment flow story generalizes; the capital stock story does not.

### 7.2 Instrument Diagnostics

The first-stage F-statistic for the gravity-predicted demographic instrument is 37.58 in the OECD subsample and 28.15 in the full sample, both well above the Staiger-Stock threshold of 10 and the Stock-Yogo critical value of 16.38 for one instrument. Instruments are strong in both samples, confirming that demographic distance is a powerful predictor of bilateral portfolio positions. We nonetheless restrict our main LP results to the OECD subsample because the absorptive capacity analysis (Section 6) shows that the investment mechanism operates only in economies with adequate institutions and financial depth.

### 7.3 FDI vs. Portfolio

In the original OECD IV specification, FDI inflows significantly predict capital deepening (β = 0.0001, p = 0.016), while portfolio inflows do not. However, this result does not survive expansion to the full panel: FDI inflows are insignificant for K/L growth across all subsamples (all p > 0.44). The FDI efficiency gap is therefore specific to the narrow OECD IV setting and should not be interpreted as a general result. The investment-employment decomposition (Section 5.4) shows that employment responds strongly to demographic inflows, complicating the mapping from investment flows to K/L outcomes. Together with the K/L sample composition findings (Section 4.1), these results suggest that the investment *flow* channel (I/Y) is the robust pathway, while the capital *stock* channel (K/L) is sensitive to sample and specification.

### 7.4 Alternative TFP Measures

Both ctfp (TFP at current PPPs) and rtfpna (TFP at constant national prices) yield the same null result: demographics do not significantly predict TFP growth at any specification.

## 8. Discussion

### 8.1 What the J-Curve Means

The two-year lag between demographic capital inflows and investment is consistent with standard models of investment adjustment. Capital arrives as financial claims (portfolio positions), requires time to be intermediated into real investment projects, and produces measurable increases in gross fixed investment with a lag. The absence of a contemporaneous effect explains why the cross-sectional literature (Prasad et al. 2007) finds that capital flows do not promote growth: contemporaneous regressions estimate β_0, missing the delayed response.

### 8.2 Why Investment but Not TFP?

Demographics predict capital quantity, not quality. The TFP null is robust across both PWT measures (ctfp and rtfpna), contemporary and lagged specifications, and every subsample we examine. This is a sobering result: demographic capital facilitates *capital widening* --- more machines per worker, more structures per unit of output --- but does not inherently drive innovation, efficiency, or technological adoption. The distinction matters for growth accounting: if demographic capital inflows raise I/GDP by 0.7--1.3 pp without improving TFP, the growth dividend comes entirely through factor accumulation, subject to diminishing returns.

The mechanism is straightforward. The lifecycle savings channel exports capital as portfolio debt --- bonds purchased by pension funds seeking yield, not venture capital seeking innovation. This capital lowers the cost of borrowing and expands the volume of intermediated credit, but it does not carry the managerial expertise, technology transfer, or competitive discipline that accompanies FDI. Our finding that FDI produces K/L deepening while portfolio flows do not (Section 7.3) reinforces this: the channel through which demographics operate (portfolio debt) is precisely the channel least likely to improve productivity.

This has implications for the convergence debate. Demographic capital flows will not close the TFP gap between rich and poor countries. Countries receiving demographic inflows will accumulate capital faster, but their productivity frontier will not shift. Over time, diminishing returns will erode the growth benefit --- consistent with the negative MPK response we document (Z₁ = −0.36, p = 0.008). Demographic capital deepening is a level effect, not a growth effect.

### 8.3 Limitations

**Pre-trend contamination.** GDP growth and TFP show significant pre-trends that resist three diagnostic approaches (controlling for recipient demographics, within-country de-meaning, and outcome residualization). This is not correctable confounding but a genuine selection pattern: countries that receive demographic capital inflows are on systematically different growth trajectories. We identify a clean causal effect only for the investment channel.

**Instrument exclusion.** Demographic distance may affect recipient outcomes through channels other than capital flows, such as trade patterns, migration, or technology diffusion. We address the exclusion restriction through three tests. First, adding trade openness as an LP control does not attenuate the J-curve (h = 2: β = 0.672, p = 0.052; attenuation of 2.9% relative to baseline). Second, controlling for remittance inflows (% GDP, from World Bank WDI) leaves the investment response unchanged (h = 2: β = 0.707, p = 0.039). Third, we test whether the instrument predicts non-financial outcomes plausibly tied to demographic distance: the instrument does significantly predict changes in working-age share (p < 0.001 at all horizons), which is expected since the instrument is constructed from demographic variables and working-age share is itself a demographic outcome. Crucially, the instrument does not predict changes in trade openness at horizons h = 0--3 (all p > 0.16), though trade openness does respond at h = 4--5 (p < 0.001), possibly reflecting a delayed real-economy response to capital flows rather than a direct violation of the exclusion restriction. The instrument is not suitable for demographic outcomes and may correlate with slow-moving structural change; our claim is narrower: it identifies a delayed investment response to the demographic component of inflows, not a clean causal effect on growth or TFP.

**OECD specificity.** Although the instrument is now strong in both the full sample (F = 28.15) and the OECD subsample (F = 37.58), the investment J-curve is concentrated in advanced economies. To verify this is not sample-specific, we stratify non-OECD countries by institutional quality. Non-OECD countries in the top half of rule of law show no significant investment response at any horizon (h = 2: β = −0.227, p = 0.59), and neither do those in the bottom half (h = 2: β = 0.132, p = 0.79). However, a pooled interaction of predicted demographic inflows with rule of law across the full sample is significant at h = 3 (β = 0.545, p = 0.049), indicating that institutional quality modulates the investment response even if the non-OECD subsamples individually lack power. The OECD restriction therefore reflects absorptive capacity, not cherry-picking or instrument weakness. Demographic capital --- arriving as portfolio debt from aging-country institutional investors --- requires deep bond markets, reliable legal enforcement of creditor rights, and sophisticated financial intermediaries to be channeled into real investment. These prerequisites are largely absent outside the OECD. Our results therefore characterize a specific mechanism --- aging-economy savings intermediated through global bond markets into OECD investment --- rather than a universal law of demographic capital allocation.

**No asset price data.** We cannot test whether demographic capital inflows that do not produce investment instead inflate asset prices. This remains an important open question.

## 9. Conclusion

Demographic forces drive international capital allocation in ways that account for significant heterogeneity in longstanding puzzles. The allocation puzzle --- capital flowing from poor fast-growing countries to rich slow-growing ones --- is concentrated in early-transition economies where demographic savings dominate. In late-transition economies, the puzzle reverses.

When demographic capital arrives in recipient countries, it does something --- but with a delay. Fixed investment increases by approximately 0.7--1.3 percentage points of GDP at a two-year horizon (depending on whether the level or first-differenced specification is used), a result that is robust to pre-trend tests and distinguishable from non-demographic gravity-driven flows. However, this capital deepening does not produce TFP gains, and it requires institutional quality and financial depth to translate into productive investment.

These findings carry implications for both theory and policy. For theory, they suggest that the lifecycle savings channel operates primarily through investment quantity rather than allocative efficiency. For policy, they suggest that countries seeking to absorb demographic capital inflows should invest in institutional quality and financial market development --- the capital will come, but its productivity depends on the recipient's absorptive capacity.

## Appendix A: LP Implementation Details

All local projections follow Jordà (2005). For **growth variables** (Δlog K/L, ΔTFP, GDP growth), the dependent variable is cumulated: $y^{cum}_{j,t+h} = \sum_{s=0}^{h} \Delta y_{j,t+s}$. For **level variables** (Investment/GDP, MPK), the dependent variable is the change from the pre-shock baseline: $y_{j,t+h} - y_{j,t-1}$. Treatment is log(predicted demographic inflows). Controls: fiscal balance/GDP, lagged NFA/GDP, log relative output per worker, KAOPEN. Estimation: PanelGLS with iterative Cochrane-Orcutt AR(1) correction.

| Variable | Transformation | Formula |
|----------|---------------|---------|
| Investment/GDP | Level lead | $y_{t+h} - y_{t-1}$ |
| Δlog(K/L) | Cumulated growth | $\sum_{s=0}^{h} \Delta\log(K/L)_{t+s}$ |
| Δlog(rnna) | Cumulated growth | $\sum_{s=0}^{h} \Delta\log(\text{rnna})_{t+s}$ |
| Δlog(emp) | Cumulated growth | $\sum_{s=0}^{h} \Delta\log(\text{emp})_{t+s}$ |
| ΔTFP | Cumulated growth | $\sum_{s=0}^{h} \Delta\log(\text{ctfp})_{t+s}$ |
| GDP growth | Cumulated growth | $\sum_{s=0}^{h} g_{t+s}$ |
| MPK proxy | Level lead | $\text{MPK}_{t+h} - \text{MPK}_{t-1}$ |
| K/Y ratio | Level lead | $(K/Y)_{t+h} - (K/Y)_{t-1}$ |

We report pre-trends at h = −3, −2, −1 for all outcomes. We omit h = −1 from some tables because the first-differenced specification for level variables mechanically links $y_t - y_{t-1}$ to the treatment at $t$, making h = −1 a tautological pre-trend. For cumulated growth variables, h = −1 is the single-period growth rate at $t - 1$, which is directly interpretable. All outcomes are reported at h = −3, −2, −1, 0, 1, 2, 3, 4, 5.

## References

- Alfaro, L., A. Chanda, S. Kalemli-Ozcan, and S. Sayek. 2004. "FDI and Economic Growth: The Role of Local Financial Markets." *Journal of International Economics* 64(1): 89--112.
- Borensztein, E., J. De Gregorio, and J.-W. Lee. 1998. "How Does Foreign Direct Investment Affect Economic Growth?" *Journal of International Economics* 45(1): 115--135.
- Durham, J.B. 2004. "Absorptive Capacity and the Effects of Foreign Direct Investment and Equity Foreign Portfolio Investment on Economic Growth." *European Economic Review* 48(2): 285--306.
- Fair, R.C., and K.M. Dominguez. 1991. "Effects of the Changing U.S. Age Distribution on Macroeconomic Equations." *American Economic Review* 81(5): 1276--1294.
- Gourinchas, P.-O., and O. Jeanne. 2013. "Capital Flows to Developing Countries: The Allocation Puzzle." *Review of Economic Studies* 80(4): 1484--1515.
- Higgins, M. 1998. "Demography, National Savings, and International Capital Flows." *International Economic Review* 39(2): 343--369.
- Jordà, Ò. 2005. "Estimation and Inference of Impulse Responses by Local Projections." *American Economic Review* 95(1): 161--182.
- Lucas, R.E. 1990. "Why Doesn't Capital Flow from Rich to Poor Countries?" *American Economic Review* 80(2): 92--96.
- Prasad, E.S., R.G. Rajan, and A. Subramanian. 2007. "Foreign Capital and Economic Growth." *Brookings Papers on Economic Activity* 2007(1): 153--209.
- Staiger, D., and J.H. Stock. 1997. "Instrumental Variables Regression with Weak Instruments." *Econometrica* 65(3): 557--586.
- Stock, J.H., and M. Yogo. 2005. "Testing for Weak Instruments in Linear IV Regression." In *Identification and Inference for Econometric Models*, edited by D.W.K. Andrews and J.H. Stock, 80--108. Cambridge University Press.
